pe 7

// project euler #7
//
// By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
//
// What is the 10,001st prime number?

// Approach I came up with after a while:
// - I remembered Sieve of Eratosthenes but couldn't figure out the exact idea without lazy lists
// - So instead I just keep track of all the previous primes and test the modulo on each prime in every loop
// - Only iterate on odd numbers, easy elimination of half the set

function nthPrime(limit) {
  var primes = [2, 3], current = 5
  for(var i = 3; i <= limit; current += 2) {
    var isPrime = true
    for(var j = 0; j < primes.length && isPrime; ++j) {
      isPrime = current % primes[j] !== 0
    }
    if(isPrime) {
      primes.push(current)
      ++i
    }
  }
  return primes[primes.length - 1]
}

module.exports = nthPrime